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\title{Summary of changes}
\author{\textit{Best effort strategy and virtual load for  asynchronous iterative load balancing}}

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\textbf{We thank the editor and both reviewers for their valuable comments and efforts which helped us improve this paper. Below, some details and answers are provided corresponding to their comments.}
 

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\section*{Reviewer  1}

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\textit{ The paper considers asynchronous load balancing algorithms based on
earlier work by Bertsekas and Tsitsiklis.
A new best effort strategy is proposed that tries to balance the load
of a node by sending some load to neighboring nodes with less load.
The goal is an even distribution of the load.
Load information messages are used between neighboring nodes to enable these
neighboring nodes to determine the amount of load to distribute in case of a
currently uneven distribution.
An experimental evaluation is provided using the SimGrid framework for different
topologies (line, torus, cube).}

\textit{
The paper is generally well written and addresses a useful problem.
The new algorithm is described in detail and it provides advantages over
the previous algorithm by Bertsekas and Tsitsiklis.
The experimental evaluation with SimGrid is detailed.
It would have been interesting to see a comparison with some of the more recent
load balancing algorithms described in the section on related work, see
references [7,9,24] as examples.
The paper needs some proof-reading due to several typos.
Nevertheless, the paper is suitable for publication.}


\textbf{We agree with the reviewer that it would be interesting to compare the algorithm's performances with other relevant existing works in the literature.
As reported in the paper, the Bertsekas and Tsitsiklis' algorithm is, to our knowledge, the closest work to the one we propose. The focus and the load balancing models addressed in [7, 9, 24] are different: Reference [7] considers partially asynchronous and static integer load balancing in homogeneous networks. The authors' work is more on the theoretical side of the spectrum, and no experimental results
are presented to validate their approach. In [9], the authors deal with dynamic networks where communication links between the resources of the network are intermittent. The work in [24] investigates the problem of allocating non divisible load applications on heterogeneous platforms and it also aims at minimizing the response time of users' jobs.}

\textbf{
We have tried to perform a second reading and check our paper as well as we could.
}

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\section*{Reviewer  2}
\textit{This paper is about a practical implementation of a strategy for iterative load balancing using a best effort strategy. The idea is to send data to the neighbors that are under the average load in order to obtain that each neighbor has exactly the average.\\
To avoid the ping-pong effect they use a k-factor to reduce the amount of load. They also distinguish between control message (metadata about the load that is going to be exchanged) and data message (actual exchanged load) that allows to have a more precise and fast estimation of the load at a given time.\\
The experiments are convincing and I like very much the discussion about the data and the conclusion drawn from them. I think the authors did a very good job in that aspect. }

\subsection*{Request 1: My only concern is the section 5.2. I did not understand clearly what is this k-factor. The authors say, "Roughly speaking...", I do not what a fuzzy explanation but I need a correct, precise and operational description of that aspect of the work. I think the authors should present a clear explanation of what they do.     
}

\textbf{The weighting system parameter k is introduced to orchestrate the right balance between the topology structure and the CCR values of the deployed application. Indeed, to speedup the convergence time of the load balancing process, we face a difficult trade-off to choose an appropriate amount of load to send between node neighbors upon load imbalance detection. On the one hand, if k is small, we expect faster convergence times for sparsely connected applications and large CCR values. On the other hand, for strongly connected applications and small CCR values, a large value of k will enable us to better balance the load locally and therefore minimize the number of iterations toward the global equilibrium. In the experiments section, we observe that choosing k in 1,2 or 4, leads to good results for the considered CCR values and the targeted topology structures: a line, a torus, and an hypercube.
}



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